This is a known issue. We're still tweaking the AI.

That I am sure is how they were landing on the hex as I have had my probes end turn on whites if they were auto moving. 

I am playing version 1.01 and I can verify that I have watched AI ships without survey modules capture all of the red nodes that are visible.  One of the unusual characteristics is that the AI ships land ON the cells with the red nodes as opposed to attacking from an ADJACENT cell.  I also noticed that the AI ships do not have to fight the defending ships, they just take the red node. A final note is that the AI ship I was watching appeared to be targeting the red nodes, not just accidentally landing on one.  I watched it move from one red node to another, so it appears to be something in the AI logic that attracts them to the red nodes.

This is not a minor bug that very few people will notice.  This is a major bug that is very noticeable and gives the impression that AI civs are getting an unfair advantage.  Please put this near the top of your list of bugs to work on.

AI fleets without survey modules have targeted and taken the red precursor anomalies without damage in my current 1.01 game.

I accidentally found a way make them regret trying to take those anomalies.  I wanted to see what kind of enemy was guarding them, so I attacked one with a tiny, armed, non-survey ship.  It is possible for the AI and you to do that.

When I made the attack, my ship was easily destroyed, and it caused the defenders to be separate from the anomaly.  They just sat there on the anomaly doing nothing but waiting.  You can try it if you want to see it happen.

Much later an AI fleet attacked the defenders.  I don't know if it was trying to survey the anomaly or just trying to attack the defenders.  Anybody was able to just attack the defenders.  All I saw was only one AI ship survive the battle, and it didn't have a survey pod.  The huge pirate ship was the only defender left, but it still had about half of its hit points.  The next turn the surviving ship, a command ship, attacked.  Both ships survived, but the command ship only had 4 hp left.  It then left.  The defending ship had about 20 hp left.  I was able to easily defeat it.

It may be a good idea to send a cheap, tiny, armed ship to attack each red anomaly to separate the defenders from the anomaly.  That way the AI will have to attack the defenders and suffer the consequences.  The huge defender is very, very powerful and will destroy all but the most powerful AI ships/fleets.  That should even things out.

AI fleets have always taken red anomalies in GC4.  They don't seem to put as much effort into them as they do the yellow anomalies.  They seem to wait until later in the game before they go after them, plus there are more yellow than red anomalies.  It is more likely a human player will see the AI take a yellow anomaly.  The best way to see them go away is to mark them with a waypoint when you find them.  Later, maybe much later, you will see the waypoint and no anomaly.

This bug also occurred inGC3, but it happened less often there.  I wonder if some of the changes made to the AI in GC4 also made the AI more likely to go after the defended anomalies.